Congressional leaders from both parties made new and competing demands Wednesday in exchange for their votes to raise the nation’s debt limit, increasing pressure on a bipartisan group attempting to negotiate a debt-reduction deal with the White House.

Top Senate Democrats, led by Majority Leader Harry M. Reid (Nev.), said they have told Vice President Biden, who is leading the talks, that any agreement on raising the legal borrowing limit must include an effort to boost the flagging economic recovery alongside deep spending cuts sought by Republicans.

The Democrats said they would prefer to see new spending on roads, bridges and other transportation projects; new investment in green energy; or additional resources for job training to show that the party is working to create jobs and lower the nation’s 9 percent unemployment rate.

They said they would also accept a payroll tax cut for employers, an idea recently floated by the White House.

The Democrats’ call came on the same day that conservative advocacy groups asked Republicans to sign a pledge saying that they vow to vote against an increase in the $14.3 trillion debt limit without sharp and immediate spending cuts, new caps on annual spending and an amendment to the Constitution that would require Congress to balance the budget.

Ten Republicans in the Senate and 10 in the House have signed the pledge, which would preclude the possibility of new spending on the economy next year.

“Politicians of all stripes, Democrats and Republicans, have spent this country to the brink of insolvency,” said Sen. Rand Paul (R-Ky.), who said he would not vote to raise the debt ceiling without winning a balanced-budget amendment.

As negotiators race to produce a bipartisan compromise before an Aug. 2 deadline, the proliferation of demands suggests that any deal could face significant obstacles on the road to final passage. In both the House and the Senate, Republicans and Democrats are splintering into a bewildering array of factions and issuing ultimatums that cannot all be met.

In the Senate, for example, a bipartisan group is pushing for a far more ambitious deal to reduce the debt. That group — led by Budget Committee Chairman Kent Conrad (D-N.D.) — is considering withholding its votes for a long-term debt-limit increase unless it sees far more than the $2 trillion in savings that has been the goal of the Biden talks.

Meanwhile, the no-taxes message of the Republican Party was underscored Wednesday by Senate Minority Leader Mitch McConnell (Ky.), who ruled out any revenue increase — even if it came through closing tax loopholes — as part of the talks. Noting that Democrats did not raise taxes on millionaires last year, when they controlled both chambers of Congress, McConnell decreed that a tax increase was even less likely now that Republicans control the House.

“They couldn’t even get that done when they owned the government. . . . So, look, taxes aren’t going to be raised,” McConnell told reporters at a breakfast held by the Christian Science Monitor.

The government needs more than $2 trillion in additional borrowing authority to pay its bills through the end of next year.

The Biden negotiators met again behind closed doors Wednesday as part of an accelerated schedule aimed at producing an agreement by the Fourth of July break.

Hours before the meeting, the nonpartisan Congressional Budget Office painted a dire picture of nation’s budget outlook, warning that the portion of the debt held by outside investors will exceed the size of the entire U.S. economy by 2021 — and nearly twice its size within 25 years — without major cuts to federal health and retirement programs or steep tax increases.

According to the CBO report, policymakers would have to come up with immediate and permanent savings of well more than $7 trillion over the next decade just to keep the debt at its current level of about 69 percent of GDP through 2035. Paying down the debt would require even more dramatic changes.

Over the long term, the CBO said, the debt will be driven by a projected explosion in spending linked entirely to Social Security, Medicare and Medicaid, as well as “insurance subsidies” that are intended to help cover the uninsured under President Obama’s new health-care law.

Tax collections could keep pace with those costs if Congress permitted tax cuts passed during the George W. Bush administration to expire on schedule in 2012 and allowed the alternative minimum tax to hit millions of additional households. But under current tax policies, the CBO said, revenue would barely cover the cost of the health and retirement programs by 2035.

Along with their competing demands, Democrats and Republicans continued to snipe at each other.

“It almost makes you wonder if they are trying to slow down the economic recovery for political gain,” Sen. Charles E. Schumer (D-N.Y.) told reporters, referring to Republicans’ cold reception to a payroll tax cut.

Republicans shot back that Democrats’ push for new stimulus is a sign that they want to find a way to use the debt talks to spend more.

“It’s a band-aid on a problem,” said Sen. Lindsey O. Graham (R-S.C.). “I want to get to the cancer — the cancer is that the institution is out of control.”

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